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In [[mathematics]], the '''Abhyankar–Moh theorem''' states that if <math>L</math> is a [[complex line]] in the complex [[Affine geometry|affine plane]] <math>\mathbb{C}^2</math>, then every embedding of <math>L</math> into <math>\mathbb{C}^2</math> extends to an [[automorphism]] of the plane. It is named after [[S. S. Abhyankar]] and T.-T. Moh, who published it in 1975. More generally, the same theorem applies to lines and planes over any [[algebraically closed field]] of [[Characteristic (algebra)|characteristic]] zero, and to certain well-behaved subsets of higher dimensional complex affine spaces. | |||
==References== | |||
*{{citation|first1=Shreeram S.|last1=Abhyankar|author1-link=S. S. Abhyankar|first2=Tzuong-Tsieng|last2=Moh|title=Embeddings of the line in the plane|journal=[[Crelle's Journal|J. Reine Angew. Math.]]|volume=276|year=1975|pages=148–166|mr=379502}}. | |||
*{{springer|id=A/a120010|title=Abhyankar–Moh theorem|author=M. Hazewinkel}} | |||
{{DEFAULTSORT:Abhyankar-Moh theorem}} | |||
[[Category:Theorems in algebraic geometry]] | |||
{{geometry-stub}} |
Revision as of 20:51, 23 December 2013
In mathematics, the Abhyankar–Moh theorem states that if is a complex line in the complex affine plane , then every embedding of into extends to an automorphism of the plane. It is named after S. S. Abhyankar and T.-T. Moh, who published it in 1975. More generally, the same theorem applies to lines and planes over any algebraically closed field of characteristic zero, and to certain well-behaved subsets of higher dimensional complex affine spaces.
References
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